Four 7.5 kg spheres are located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the gravitational force on one sphere due to the other three.
R=.6M
mass=7.5 kg
Going clockwise label the masses in a square. M1 top left corner, M2 top right corner, M3 bottom right corner, M4 bottom left corner.
Start with M1 and M2 use Newton's universal gravity formula;
F=G((M1*M2)/r^2)
Where G always equals 6.67*10^-11
Back to M1 and M2
equation:
Fg=6.67*10^-11((7.5kg*7.5kg)/0.6m^2)
Fg=1.04*10^-8 @ 0°
Same exact thing for M1 and M4 but instead of 0° it's 270°
For M1 and M3 it's a diagonal radius so to solve for the Diagonal radius make a right triangle and use the equation a^2+b^2=c^2 where c^2 is what we are finding.
Equation:
.6^2+.6^2=c^2
.72=c^2
Square root.72 To get the radius of .84
Now solve M1 and M3
Equation:
Fg=6.67*10^-11((7.5kg*7.5kg)/0.84m^2)
Fg=5.31*10^-9 @ 315°
Now you have to add the vectors to get the vector of C^2 by making a right triangle connecting M1,M2,M3 making M2 where the 90° is
From M1 to M2 we already know it's 1.04*10^-8 but she still need to find the cos to find the other part of the line.
Equation:
Cos(45=x/5.31*10^-9
X=3.75*10^-9
Y (aka M2 to M3) equals the same because 45 makes sin and cos the same
After finding that add
(1.04*10^-8)+(3.75*10^-9)
Getting; 1.41*10^-8 Remember both lines M1 to M2 and M2 to M3 are equal so they are both 1.41*10^-8
With that said to finalize this problem find C^2 now
Equation:
(1.41*10^-8)^2 + (1.41*10^-8)^2 =C^2
4.00*10^-16=CA
square root 4.00*10^-16 and you should get 2.0*10^-8
ANSWER: 2.0*10^-8 @ 45°
Thanks Tiffany! I wish my teacher could actually teach me this instead of puffing the devil' so lettuce...
I had been looking online for the answer to this question for 3 hours and this is the only process that I found was right THANK YOU
You're a blessing Tiffany :D You save me ^_^
This saved me! None of the other processes online were right but this one!
I have been looking at the note from my class and could not figure out how to solve this equation. THANK YOU for breaking down the process in an easy way to understand!!
Thank you so much! This helped a lot.
To calculate the gravitational force on one sphere due to the other three, we need to use the equation for the gravitational force between two objects:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we have four spheres and we want to find the force on one sphere due to the other three. So we need to calculate the force between the spheres individually and then add them up.
To find the magnitude of the gravitational force between two spheres, we can use the equation above.
Step 1: Calculate the force between one sphere and another sphere.
F1 = (G * m1 * m2) / r^2
Step 2: Repeat Step 1 for the other two spheres.
F2 = (G * m1 * m3) / r^2
F3 = (G * m1 * m4) / r^2
Step 3: Add up the forces to find the total force.
F_total = F1 + F2 + F3
Now let's plug in the values given in the problem:
m1 = 7.5 kg (mass of one sphere)
m2 = 7.5 kg (mass of another sphere)
m3 = 7.5 kg (mass of the third sphere)
m4 = 7.5 kg (mass of the fourth sphere)
r = 0.60 m (distance between the centers of the spheres)
Now we can calculate the magnitude of the gravitational force:
F1 = (6.67430 × 10^-11 N m^2/kg^2 * 7.5 kg * 7.5 kg) / (0.60 m)^2
F2 = (6.67430 × 10^-11 N m^2/kg^2 * 7.5 kg * 7.5 kg) / (0.60 m)^2
F3 = (6.67430 × 10^-11 N m^2/kg^2 * 7.5 kg * 7.5 kg) / (0.60 m)^2
F_total = F1 + F2 + F3
Now, to find the direction of the gravitational force, we need to consider the vector nature of the force. Since the spheres are located at the corners of a square, the forces would have components in both the horizontal and vertical directions. To find the overall direction, we need to calculate the components of each force and add them up vectorially.
Please note that to determine the actual values, you need to perform the calculations using these formulas and the given values.